Ok, humbucker pickups are, if you didn't know, 2 single coil pickups wired in series. The trick is that the magnetic pole pieces in one coil are oriented with the N magnetic pole facing the strings and the other coil with the S magnetic pole facing the strings making the 2 coils magnetically opposite. Since they are in series and of opposite polarity or phase, they reduce noise caused by interference by common-mode rejection.
This helps to greatly reduce the hum you hear when using single coils at higher gain levels. There are a couple of side effects of using dual coils in this way that are not necessarily undesirable. The most noticeable is that the output is higher. The more subtle, but what we're concerned with here, is the different tonal characteristics.
Since the 2 coils of the humbucker are wired in series, that means that one side of each coil is connected together, the other wire on coil #1 goes to ground, and the other wire on coil #2 is the output signal. So, if you connect a wire to the place where the 2 coils connect together and then connect that new wire to ground... coil #1 is grounded on both sides effectively eliminating it from the circuit leaving coil #2 to operate by itself! Have a look at the schematic pics... Simple right?
To go back and forth between single coil and humbucker operation we need to simply add a switch in that new wire!
Back to tonal characteristics for a minute. Obviously, since we took half of the magnets and half of the coil windings out of the circuit we now have half of the output (but not half volume because your ear's response to loudness logarithmic rather than linear, but that's another matter.) Notice that a coil of wire is an inductor and we took half of the inductance out too! The instrument cables we all use have inherent capacitance (about 15-30 pF per foot or so) that creates a tuned circuit with your inductive pickups! This tuned circuit varies with different cables and pickups and can produce a slight boost in the mids and roll off the highs depending on cable length and pickup inductance... The options described below could allow you to vary this tuning to change the frequency response of you rig.
To start really tweaking we could go a step further and add resistor to the wire. The greater the value of the resistance the more of Coil #1's signal will go through coil #2 and the more influence coil #1 will have to the overall circuit. With very low resistance here, coil #1 will have an easier path to ground, so it will have much less influence.
Want more? Why not make the resistor variable? Now coil #1 can influence the circuit as much or as little as we want!
Refer to the schematic pics for these options because I didn't do this on my guitar seen in the pics, and most of this is difficult to describe in writing. (The schematics do not show any volume/tone controls or pickup switching because every instrument will be different). I didn't have the desire or the space to add this much control, but I do want you to understand what is possible. It would take virtually no space to add a fixed resistor to tune the amount of coil #1 in the circuit, but I have not experimented with values for this resistor. If you wanted to try, I think the best way would be to temporarily wire a 1M or a 500K or so variable resistor and play with it until you find a setting you like. Then use a multimeter to measure the value and replace it with the nearest standard value resistor to complete the permanent installation.
If you try some of these options, I hope to see a report in the comments section! It would be very cool to hear about the results people are getting with different configurations.